Displaying similar documents to “Superposition of imbeddings and Fefferman's inequality”

Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let n ≥ 2 and Ω ⊂ ℝ n be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space W 0 L Φ ( Ω ) , where the Young function Φ behaves like t n log α ( t ) , α < n - 1 , for t large, into the Zygmund space Z 0 n - 1 - α n ( Ω ) . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space W 0 m L n m , q log α L ( Ω ) , m < n , q ∈ ( 1 , ∞ ] , α < 1 q ' , embedded into the Zygmund space Z 0 1 q ' - α ( Ω ) .

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.